A Digital Flatness-based Control System of a DC Motor

Abstract: In this paper, an approach to design and implement a real-time system based on a RISC microcontroller dedicated to a DC motor speed control, is proposed. A polynomial RST controller based on the flatness property of linear systems is implemented in C/C++ embedded programming language. The flatness property is used in order to design a robust controller with high performance in terms of tracking. The proposed controller is then applied to control a DC motor. The simulation and experimental results underline the efficiency of the flatness-based polynomial controller in a real-time control framework.

Mounir Ayadi graduated from Ecole Nationale d’Ingénieurs de Tunis in 1998 and received his PhD degree in Automatic Control from the Institut National Polytechnique de Toulouse in 2002. He was a post-doctoral fellow at the Ecole Supérieure d’Ingénieurs en Génie Electrique de Rouen in 2003. He is currently Maître-Assistant at the Ecole Nationale d’Ingénieurs de Tunis. His research interests are in the area of control system theory, predictive and adaptive control, and flat systems.

Joseph Haggège graduated from Ecole Nationale d’Ingénieurs de Tunis and received the PhD degree in Electrical Engineering in 1998 and 2003, respectively. He is currently Maître-Assistant at the Ecole Nationale d’Ingénieurs de Tunis. His research interests are in the area of fuzzy, neural and neuro-fuzzy control, and embedded systems.

Soufiène Bouallègue received the Engineer Diploma degree in Electrical Engineering and the Master in Automatic Control from Ecole Nationale d’Ingénieurs de Tunis in 2006 and 2007, respectively.

Mohamed Benrejeb has obtained the Diploma of “Ingénieur IDN” (French “Grande Ecole”) in 1973, the Master degree of Automatic Control in 1974, the PhD in Automatic Control of the University of Lille in 1976 and the DSc of the same University in 1980. He is currently a full Professor at the Ecole Nationale d’Ingénieurs de Tunis and an invited Professor at the Ecole Centrale de Lille. His research interests are in the area of analysis and synthesis of complex systems based on classical and non conventional approaches.

The possibility of varying or reversing the rotation speed of motors constitutes a necessity in industrial domain and in process automation. In this framework, the use of a DC motor can be a good solution. However, the speed control presents some delicate problems, particularly in terms of robustness, of perturbation rejection and especially when tracking trajectory. In this case, it is interesting to consider adequate control laws for the drive. Several techniques of control theory systems using conventional and non conventional methods have been applied on such type of motor [16][22][24][28].

The flatness property, introduced in 1992, presents a new point of view in the control theory domain [1-10]. This property, developed initially in the nonlinear continuous-time case, defines a class of systems well known as flat systems. The existence of a variable called flat or linearizing output allows to define all other system variables. In the linear case [3][4], it is sufficient to consider the Brunovsky’s outputs of the canonical controllability form like the flat outputs [30][31]. Thus, the dynamic of such a process can be deduced without solving differential equations. Therefore, it is possible to express the state, as well as the input system, as differential functions of the flat output. The main contribution of the flatness that will be exploited in this paper is the effective trajectory planning and tracking solutions with high performances specification.

The flatness property of DC motor model will be used to obtain of a closed-loop system with high performances by designing a robust polynomial RST controller with an argued choice for its design. The tracking of a reference trajectory, function of the flat output system, as well as the rejection of disturbances and noises of measure, will be the goal of this controller.

On the other hand, the evolutions in the micro-electronics field, especially in the domain of digital signals processors are at the origin of many progresses in power electronics. Many works in the control theory domain have shown the performances of DSP (Digital Signal Processor) integration, microcontrollers (PIC, AVR…) or as digital components like FPGA or ASIC. The development of built-in digital controller on programmable target PIC 16F876 presents an advantage of fast real-time implementation of the control algorithms as well as the reduction in terms of components number and bulk [12-14].

In this paper, an approach to design such a control system as well as its hardware architecture is presented. A software integration of the developed RST algorithm, relative to the computer tools bound to this type of built-in circuits in embedded programming C/C++ language is implemented in a real-time environment.

6. Conclusion

An application of concepts, methods and specific tools to the design and the implementation of real-time systems to control processes has been considered in this paper. The feasibility of the real-time controller with a high performance in terms of tracking, is the principal contribution.

While basing on analytic procedures, the flatness control of the DC drive has led to a robust polynomial controller. However, the exploitation of performances in tracking a reference trajectory and in rejection of additive load disturbances as well as the simplicity of implementation represent arguments that justify the choice of a such technique of advanced automatic control. The design of the RST polynomial controller using the flatness property of the plant, is guided by the choice of the tracking dynamics. The robustness of the developed controller with regards to modelling uncertainties as well as the intervention of disturbance and noises in the control, is guaranteed.

The implemented control algorithm led to satisfactory experimental results close to those obtained by simulation. It remains to illustrate effects of additive disturbance using validation experiment in real-time framework.

Haggège, J., M. Benrejeb and P. Borne, A New Approach for On-line Optimisation of a Fuzzy Controller, In Proceedings of the 8th IEEE International Conference on Electronics, Circuits and Systems, Vol. 2, Malta, 2001, pp. 971-975.